TSTP Solution File: SET654+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET654+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 06:37:46 EDT 2022
% Result : Theorem 0.47s 0.66s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET654+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 16:04:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.47/0.66 (* PROOF-FOUND *)
% 0.47/0.66 % SZS status Theorem
% 0.47/0.66 (* BEGIN-PROOF *)
% 0.47/0.66 % SZS output start Proof
% 0.47/0.66 Theorem prove_relset_1_16 : (forall B : zenon_U, ((ilf_type B (set_type))->(forall C : zenon_U, ((ilf_type C (set_type))->(forall D : zenon_U, ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type D B))->((subset B C)->(ilf_type E (relation_type D C))))))))))).
% 0.47/0.66 Proof.
% 0.47/0.66 assert (zenon_L1_ : forall (zenon_TE_ba : zenon_U) (zenon_TB_bb : zenon_U) (zenon_TD_bc : zenon_U), (forall D : zenon_U, ((ilf_type D (relation_type zenon_TD_bc zenon_TB_bb))->((subset (domain_of D) zenon_TD_bc)/\(subset (range_of D) zenon_TB_bb)))) -> (ilf_type zenon_TE_ba (relation_type zenon_TD_bc zenon_TB_bb)) -> (~(subset (range_of zenon_TE_ba) zenon_TB_bb)) -> False).
% 0.47/0.66 do 3 intro. intros zenon_H17 zenon_H18 zenon_H19.
% 0.47/0.66 generalize (zenon_H17 zenon_TE_ba). zenon_intro zenon_H1d.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.47/0.66 exact (zenon_H1f zenon_H18).
% 0.47/0.66 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 0.47/0.66 exact (zenon_H19 zenon_H20).
% 0.47/0.66 (* end of lemma zenon_L1_ *)
% 0.47/0.66 assert (zenon_L2_ : forall (zenon_TB_bb : zenon_U) (zenon_TC_bn : zenon_U) (zenon_TE_ba : zenon_U), (forall C : zenon_U, ((ilf_type C (set_type))->((subset (range_of zenon_TE_ba) C)<->(forall D : zenon_U, ((ilf_type D (set_type))->((member D (range_of zenon_TE_ba))->(member D C))))))) -> (ilf_type zenon_TC_bn (set_type)) -> (~(subset (range_of zenon_TE_ba) zenon_TC_bn)) -> (forall D : zenon_U, ((ilf_type D (set_type))->((member D (range_of zenon_TE_ba))->(member D zenon_TB_bb)))) -> (forall D : zenon_U, ((ilf_type D (set_type))->((member D zenon_TB_bb)->(member D zenon_TC_bn)))) -> False).
% 0.47/0.66 do 3 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H25 zenon_H26.
% 0.47/0.66 generalize (zenon_H22 zenon_TC_bn). zenon_intro zenon_H28.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 0.47/0.66 exact (zenon_H2a zenon_H23).
% 0.47/0.66 apply (zenon_equiv_s _ _ zenon_H29); [ zenon_intro zenon_H24; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H2b ].
% 0.47/0.66 apply (zenon_notallex_s (fun D : zenon_U => ((ilf_type D (set_type))->((member D (range_of zenon_TE_ba))->(member D zenon_TC_bn)))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ].
% 0.47/0.66 elim zenon_H2e. zenon_intro zenon_TD_bv. zenon_intro zenon_H30.
% 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 0.47/0.66 generalize (zenon_H26 zenon_TD_bv). zenon_intro zenon_H35.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 0.47/0.66 exact (zenon_H37 zenon_H32).
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ].
% 0.47/0.66 generalize (zenon_H25 zenon_TD_bv). zenon_intro zenon_H3a.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H37 | zenon_intro zenon_H3b ].
% 0.47/0.66 exact (zenon_H37 zenon_H32).
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 0.47/0.66 exact (zenon_H3d zenon_H34).
% 0.47/0.66 exact (zenon_H39 zenon_H3c).
% 0.47/0.66 exact (zenon_H33 zenon_H38).
% 0.47/0.66 exact (zenon_H24 zenon_H2c).
% 0.47/0.66 (* end of lemma zenon_L2_ *)
% 0.47/0.66 apply NNPP. intro zenon_G.
% 0.47/0.66 apply (zenon_notallex_s (fun B : zenon_U => ((ilf_type B (set_type))->(forall C : zenon_U, ((ilf_type C (set_type))->(forall D : zenon_U, ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type D B))->((subset B C)->(ilf_type E (relation_type D C))))))))))) zenon_G); [ zenon_intro zenon_H3e; idtac ].
% 0.47/0.66 elim zenon_H3e. zenon_intro zenon_TB_bb. zenon_intro zenon_H3f.
% 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40.
% 0.47/0.66 apply (zenon_notallex_s (fun C : zenon_U => ((ilf_type C (set_type))->(forall D : zenon_U, ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type D zenon_TB_bb))->((subset zenon_TB_bb C)->(ilf_type E (relation_type D C))))))))) zenon_H40); [ zenon_intro zenon_H42; idtac ].
% 0.47/0.66 elim zenon_H42. zenon_intro zenon_TC_bn. zenon_intro zenon_H43.
% 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H23. zenon_intro zenon_H44.
% 0.47/0.66 apply (zenon_notallex_s (fun D : zenon_U => ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type D zenon_TB_bb))->((subset zenon_TB_bb zenon_TC_bn)->(ilf_type E (relation_type D zenon_TC_bn))))))) zenon_H44); [ zenon_intro zenon_H45; idtac ].
% 0.47/0.66 elim zenon_H45. zenon_intro zenon_TD_bc. zenon_intro zenon_H46.
% 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47.
% 0.47/0.66 apply (zenon_notallex_s (fun E : zenon_U => ((ilf_type E (relation_type zenon_TD_bc zenon_TB_bb))->((subset zenon_TB_bb zenon_TC_bn)->(ilf_type E (relation_type zenon_TD_bc zenon_TC_bn))))) zenon_H47); [ zenon_intro zenon_H49; idtac ].
% 0.47/0.66 elim zenon_H49. zenon_intro zenon_TE_ba. zenon_intro zenon_H4a.
% 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H4a). zenon_intro zenon_H18. zenon_intro zenon_H4b.
% 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c.
% 0.47/0.66 generalize (p3 zenon_TB_bb). zenon_intro zenon_H4e.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ].
% 0.47/0.66 exact (zenon_H50 zenon_H41).
% 0.47/0.66 generalize (zenon_H4f zenon_TC_bn). zenon_intro zenon_H51.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H2a | zenon_intro zenon_H52 ].
% 0.47/0.66 exact (zenon_H2a zenon_H23).
% 0.47/0.66 generalize (zenon_H52 zenon_TD_bc). zenon_intro zenon_H53.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.47/0.66 exact (zenon_H55 zenon_H48).
% 0.47/0.66 generalize (zenon_H54 zenon_TE_ba). zenon_intro zenon_H56.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H1f | zenon_intro zenon_H57 ].
% 0.47/0.66 exact (zenon_H1f zenon_H18).
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H24 | zenon_intro zenon_H58 ].
% 0.47/0.66 generalize (p6 (range_of zenon_TE_ba)). zenon_intro zenon_H59.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H5a | zenon_intro zenon_H22 ].
% 0.47/0.66 generalize (p22 (range_of zenon_TE_ba)). zenon_intro zenon_H5b.
% 0.47/0.66 exact (zenon_H5a zenon_H5b).
% 0.47/0.66 generalize (zenon_H22 zenon_TB_bb). zenon_intro zenon_H5c.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H5d ].
% 0.47/0.66 exact (zenon_H50 zenon_H41).
% 0.47/0.66 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H19; zenon_intro zenon_H5e | zenon_intro zenon_H20; zenon_intro zenon_H25 ].
% 0.47/0.66 generalize (p2 zenon_TD_bc). zenon_intro zenon_H5f.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H55 | zenon_intro zenon_H60 ].
% 0.47/0.66 exact (zenon_H55 zenon_H48).
% 0.47/0.66 generalize (zenon_H60 zenon_TB_bb). zenon_intro zenon_H61.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H50 | zenon_intro zenon_H17 ].
% 0.47/0.66 exact (zenon_H50 zenon_H41).
% 0.47/0.66 apply (zenon_L1_ zenon_TE_ba zenon_TB_bb zenon_TD_bc); trivial.
% 0.47/0.66 generalize (p13 zenon_TB_bb). zenon_intro zenon_H62.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H50 | zenon_intro zenon_H63 ].
% 0.47/0.66 exact (zenon_H50 zenon_H41).
% 0.47/0.66 generalize (zenon_H63 zenon_TC_bn). zenon_intro zenon_H64.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H2a | zenon_intro zenon_H65 ].
% 0.47/0.66 exact (zenon_H2a zenon_H23).
% 0.47/0.66 apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H68; zenon_intro zenon_H67 | zenon_intro zenon_H66; zenon_intro zenon_H26 ].
% 0.47/0.66 generalize (p6 zenon_TB_bb). zenon_intro zenon_H69.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H50 | zenon_intro zenon_H6a ].
% 0.47/0.66 exact (zenon_H50 zenon_H41).
% 0.47/0.66 generalize (zenon_H6a zenon_TC_bn). zenon_intro zenon_H6b.
% 0.47/0.66 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ].
% 0.47/0.66 exact (zenon_H2a zenon_H23).
% 0.47/0.66 apply (zenon_equiv_s _ _ zenon_H6c); [ zenon_intro zenon_H6d; zenon_intro zenon_H67 | zenon_intro zenon_H4d; zenon_intro zenon_H26 ].
% 0.47/0.66 exact (zenon_H6d zenon_H4d).
% 0.47/0.66 exact (zenon_H67 zenon_H26).
% 0.47/0.66 apply (zenon_L2_ zenon_TB_bb zenon_TC_bn zenon_TE_ba); trivial.
% 0.47/0.66 exact (zenon_H4c zenon_H58).
% 0.47/0.66 Qed.
% 0.47/0.66 % SZS output end Proof
% 0.47/0.66 (* END-PROOF *)
% 0.47/0.66 nodes searched: 9442
% 0.47/0.66 max branch formulas: 3176
% 0.47/0.66 proof nodes created: 676
% 0.47/0.66 formulas created: 44384
% 0.47/0.66
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